These puzzles were asked in online contest ENIGMA’11 in Krukshetra’11 by Anna University on 8th of jan. Try to solve these puzzles.. Really amazing..
Enigma SET 1 : JAN 08,2011 20:30 HRS [IST]
Question 1:
Average of 6 distinct positive integers is 33. The median of the three largest numbers is 43. What is the difference between the highest and lowest possible median of the 6 numbers?
Question 2:
In class A, the ratio of boys to girls is 2:3. In class B the ratio of boys to girls is 4 : 5. If the ratio of boys to girls in both classes put together is 3 : 4, what is the ratio of number of girls in class A to number of girls in class B?
Question 3:
e f
a b c d
g h
The grid is filled with numbers from 11 to 18, inclusive such that no 2 adjacent cells have consecutive numbers. Any two cells that share either a side or a vertex are adjacent. What is the value of a + b + c + d?
Question 4:
Letters of the English alphabet are randomly assigned values from 1 to 26, inclusive. Each letter is assigned a unique value and no two letters are assigned the same value. Each word has a score that is equal to the product of the scores of the letters in it. Scores of a few words are given below.
a. EARTH = 120
b. EAT = 24
c. HALT = 72
d. LACE = 336.
If the score of REALLY is a perfect square, find Y?
Question 5:
Set S contains elements a, b, c, d, e, f, g, h, and i. Each of these elements corresponds to values from 1 to 9. Furthermore the following is known
a. d * e, e * h and h * d are elements in the set
b. g – i = b – a
c. c – f – a is an element in the set
d. b – e, b – h and g – d are all prime
What is the value of a * f * i?
Question 6:
Three thieves looted a bank and got ‘n’ gold coins. That night the thieves took turns watching the gold coins. The first watcher decided to divide the coins into 3 equal piles. When he did this, he found he had one remaining coin. He took this extra coin, took one of the piles, and left the remaining coins in one big pile. During the second thief’s turn, he also divided the loot into three piles, found one coin left out, kept the extra coin and one of the piles for himself and heaped up the remaining into 1 pile. The last thief also did the same thing. What is the smallest number of coins there could have been in the original pile?
Question 7:
In a classroom, a teacher notices that all the ‘m’ students were January-born. He walks into the classroom and tells the students that if no two students shared a birthday, he would take the entire class out for dinner, but if some two students shared a birthday the class should take him out for dinner. What should be the minimum value of ‘m’ for the teacher to have a more than even chance of winning the bet?
Question 8:
A win gets a team 2 points, a draw gets a team 1 point and a loss 0 points. India and South Africa play a series of 3 matches, what is the probability that India will get exactly three points? Probability of India winning a match is 0.4, probability of a draw = 0.3.
Question 9:
N is an 80-digit positive integer (in the decimal scale). All digits except the 44th digit (from the left) are 2. If N is divisible by 13, find the 44th digit.
Question 10:
A man wants to leave his wealth for his 5 sons and/or 11 grandchildren. He realizes that if he distributes his wealth equally amongst his sons, he has $2 left. If he distributes it equally amongst his grand kids, he has $3 left. If he distributes it equally among all his progeny, he has $4 left. What is the least amount of money the old man might be leaving behind?
Question 11:
A page is torn from a novel. The sum of the remaining digits is 10000. What is the sum of the two page-numbers on the torn page of this novel?
Question 12:
A number n! is written in base 6 and base 8 notation. Its base 6 representation ends with 10 zeroes. Its base 8 representation ends with 7 zeroes. Find the smallest n that satisfies these conditions
Question 13:
[x] is the greatest integer less than or equal to x. Find the number of positive integers n such that [n/11] = [n/13].
Question 14:
Positive numbers 1 to 55, inclusive are placed in 5 groups of 11 numbers each. What is the maximum possible average of the medians of the 5 groups?
Question 15:
How many 5 digit numbers exist, comprising the digits 1, 2, 3, 4, 5 each occurring exactly once that such that ‘1’ does not appear immediately before ‘2’, but are divisible by 12. (Ex. 34152 would be counted, whereas 34512 would not be counted)
Question 16:
If x is chosen at random from the range 0 < x < 3, what is the probability that [x], [2x] and [3x] are NOT in arithmetic progression. [x] is the greatest integer less than or equal to x.
Question 17:
The ages of 4 brothers are a, b, c and d. We know the following about their ages:
a. Exactly 3 of the 4 are prime
b. Exactly 3 are odd
c. If we took the ages two at a time and added them, exactly 3 of the 6 sums are prime
d. Exactly three of the squares of the ages are less than 75
e. The product of the 4 ages has exactly 16 factors
What is the sum of the 4 ages?
Question 18:
Two professors P and Q meet. It is known that they each have 2 kids and the ages of all 4 kids lie between 1 and 10, inclusive. They also know that the ages of all 4 kids are distinct. The following conversation occurs between the two professors
a. P: The sum of the ages of my kids is a prime number
b. Q: The sum of the ages of my kids is also a prime number
c. P: The ages of my kids is composite
d. Q: That is interesting. I can say that my son is elder than both your kids, but cannot say for sure that my daughter is younger than both your kids
e. P: I know the ages of both your kids now, and your daughter is not younger than both my kids
f. Q: Thanks. I also know the ages of both your kids
What is the sum of the 4 ages?
Question 19:
A circle of radius 5 cms has two chords AB and BC of length 6 cms each. What is the length of chord AC?
Question 20:
A rectangle is constructed of lengths 19 and 15 units. Find the maximum number of rectangles that can be inscribed in it having odd unit lengths.
see this link for upcoming online puzzles contests on Click Here!
Enigma SET 2 : JAN 15,2011 20:30 HRS [IST]
Enigma SET 3 : JAN 22,2011 20:30 HRS [IST]
